The sum of coefficients of bounded univalent functions

We solve the maximal value problem for the functional in the class of functionsf(z)=z+a ₂z²+… that are holomorphic and univalent in the unit disk and satisfy the inequality |f(z)|<M. We prove that the Pick functions are extremal for this problem for sufficiently largeM whenever the set of indicesk ₁,…,k_m contains an even number. Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 728–733, May, 1997. Translated by S. S. Anisov     

Best approach regions for potential spaces

We characterize the approach regions so that the non-tangential maximal function is of weak-type on potential spaces, for which we use a simple argument involving Carleson measure estimates.

     

Potential Operators,Maximal Functions,and Generalizations of A ∞

We derive weighted norm estimates which relate integral operators of potential type (fractional integrals) to corresponding maximal operators (fractional maximal operators). We also derive norm estimates for the maximal operators. The conditions that we impose on the weights involve A conditions of content type which are weaker than the usual A condition. The analysis is carried out in the context of spaces of homogeneous type.     

Weighted rearrangement inequalities for local sharp maximal functions

Several weighted rearrangement inequalities for uncentered and centered local sharp functions are proved. These results are applied to obtain new weighted weak-type and strong-type estimates for singular integrals. A self-improving property of sharp function inequalities is established.

     

A counterexample to a weak-type estimate for potential spaces and tangential approach regions

We show that for every potential space , there exists an approach region for which the associated maximal function is of weak-type, but the boundedness for the completed region is false, which is in contrast with the nontangential case.

     

A generalization of the strong Fitzpatrick inequality

We present a generalization of the strong Fitzpatrick inequality in the context of reflexive Banach spaces, involving a twisted bigger conjugate function. We also introduce a related family of gap functions for maximal monotone inclusion problems.     

Chow-Type Maximal Inequality for Conditional Demimartingales and Its Applications

In this paper, the Chow-type maximal inequality for conditional demimartingales is established. By using the Chow-type maximal inequality, the authors provide the maximal inequality for conditional demimartingales based on {concave Young functions}. At last, the moment inequalities for conditional demimartingales are established.     

There do not exist minimal algebras between C*(X) and C(X) with prescribed real maximal ideal spaces

Let C(X) be the algebra of all real-valued continuous functions on a completely regular Hausdorff space X, and C*(X) the subalgebra of bounded functions. We prove that for any intermediate algebra A between C*(X) and C(X), other than C*(X), there exists a smaller intermediate algebra with the same real maximal ideals as in A. The space X is called A-compact if any real maximal ideal in A corresponds to a point in X. It follows that, for a noncompact space X, there does not exist any minimal intermediate algebra A for which A is A-compact. This completes the answer to a question raised by Redlin and Watson in 1987.     

Tangential Boundary Behaviour of Harmonic Functions on Trees

We study the behaviour of harmonic functions on a homogeneous tree from the point of view of the tangential boundary covergence.     

Algebras between C *(X) and C(X) that are closed under countable composition

Let be the algebra of all real-valued continuous functions on a completely regular space X, and the subalgebra of bounded functions. We show that the space of real maximal ideals of an intermediate algebra between and is a -embedded closed subspace of the product of with a product of copies of the real line. We make use of this embedding to provide a new characterization of the intermediate algebras that are closed under countable composition, and to exhibit an example of an intermediate algebra on that is closed under countable composition but not isomorphic to any .     

Maximal Monotone Operators, Convex Functions and a Special Family of Enlargements

This work establishes new connections between maximal monotone operators and convex functions. Associated to each maximal monotone operator, there is a family of convex functions, each of which characterizes the operator. The basic tool in our analysis is a family of enlargements, recently introduced by Svaiter. This family of convex functions is in a one-to-one relation with a subfamily of these enlargements. We study the family of convex functions, and determine its extremal elements. An operator closely related to the Legendre–Fenchel conjugacy is introduced and we prove that this family of convex functions is invariant under this operator. The particular case in which the operator is a subdifferential of a convex function is discussed.     

On a class of subalgebras of and the intersection of their free maximal ideals

Let be a Tychonoff space and a subalgebra of containing . Suppose that is the set of all functions in with compact support. Kohls has shown that is precisely the intersection of all the free ideals in or in . In this paper we have proved the validity of this result for the algebra . Gillman and Jerison have proved that for a realcompact space , is the intersection of all the free maximal ideals in . In this paper we have proved that this result does not hold for the algebra , in general. However we have furnished a characterisation of the elements that belong to all the free maximal ideals in . The paper terminates by showing that for any realcompact space , there exists in some sense a minimal algebra for which becomes -compact. This answers a question raised by Redlin and Watson in 1987. But it is still unsettled whether such a minimal algebra exists with respect to set inclusion.

     

Maximal monotonicity, conjugation and the duality product

Recently, the authors studied the connection between each maximal monotone operator and a family of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities.

The aim of this paper is to establish the converse of the latter fact. Namely, that every convex function satisfying those two particular inequalities is associated to a unique maximal monotone operator.

     

加权BMO函数空间上的Hardy－Littlewood极大算子

本文给出了Ｈａｒｄｙ－Ｌｉｔｔｌｅｗｏｏｄ极大函数和加权ＢＭＯ的有界性证明：即若f∈ＢＭＯ_w,w∈A_∞,且(?)Mf(x)<∞, 则M(f)(x) ∈BMO_w, 且‖Mf‖_w^*≤c‖f‖_w^*.     

向量值哈代-洛伦茨空间

对于1r∞与巴拿哈空间B=L~r(Ω,F,μ),我们研究了欧几里得空间R~n上B-值缓分布构成的哈代-洛伦茨空间H~(p,q)(R~n,B)及哈代-洛伦茨空间之间的内插,其中0p∞和0q≤∞,获得了H~(p,q)(R~n,B)的一系列等价的刻画及其原子分解.若Ω={1},则H~(p,q)(R~n,B)=H~(p,q)(R~n)是经典的情形;若Ω=Z是整数集且μ是Z上的计数测度并且r=2,0p∞及q=∞,则H~(p,q)(R~n,B)=H~(p,∞)(R~n,e~2)转化为Grafakos和He在文[Weak Hardy spaces,Preprint,2014]中讨论的情形.     

θ-型Calderón-Zygmund算子多线性交换子的加权估计

讨论了θ-型Calderón-Zygmund算子T与b=(b_1,b_2,…,b_m)(b_j∈Osc_(exp L~Tj),1≤j≤m)生成的多线性交换子(?)的加权估计.当0相似文献   

Some characterizations of

We show that a function on the unit disk extends continuously to , the maximal ideal space of iff it is uniformly continuous (in the hyperbolic metric) and close to constant on the complementary components of some Carleson contour.